= Lee ee Ee Ree ee eg Ea ee ee Ce EE Ne Plater SRE 
_ Report of Messrs. Humphreys and Abbot. 37 
An up-stream wind, by diminishing the velocity at the surface, 
ereates a slight increase of slope; and this would increase the 
mean velocity of the stream, but for the fact that, as much as 
the new slope would add, the wind destroys, so that the mean 
velocity remains constant, What the wind destroys at the sur- 
face must therefore be compensated at the bottom; and, as these 
effects are propagated through the mass according to the same 
laws as the ordinary resistances, the curve of velocities continues 
to be parabolic, but the level of its axis is changed. 
The simplicity of ~W fen suggests an improved method of 
gauging streams; but into these practical details it is eo im- 
portant that we should aise: here 
e may here convenientl resent, in a single group, the 
most important of the formule which result £ from the investiga- 
tions of which we have been endeavoring to give an account. 
Those which have not been fully explained, are easily deduci- 
ble from those which have. 
V=Va— (bv)? ( <5) ‘< Veeve, —@)(Z), 
Vi»=Va,— (50)*( 1 —<). Vio= otis (0)?. 
2 1 ld 
V.—= gv arts Vots5 (Vo esa V>)- 
= Vite) ‘(eS =~. 
v2v i+: (oj# (PAD 4)-a024—d) 
d,=(0°317-+0°06f)r. U,,==0°93». 
U,=0-930-+(0-016—0-06f) (bv). 
U,=20-980-+-(0-06f— 0350)(60)?. 
Va=0-930+( (0°31 7-+.0-06f)? —0-06f-++0-01 8 )(bw)8. 
a “ 0-06/-.0016) 
v=((1 -08Uyr-+-0-0028)* — o-04s8*)?. 
(To be continued.) 
Sd 
